Finite Group Databasebeta

← C2×#11738364 #14232338

Subgroups — C2×#11738364 #14232338

Order 1792.

1878 conjugacy classes of subgroups.

The subgroup lattice has 720 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#90330C211yesmaximal, characteristic
2C2×#90326C211yesmaximal, characteristic
3C2×C7×#470C211yesmaximal, characteristic, complemented
4C2×#89960C211yesmaximal, characteristic, complemented
5C2×#89956C211yesmaximal, characteristic, complemented
6C2×#89899C211yesmaximal, characteristic
7C2×#89893C211yesmaximal, characteristic, complemented
8C2×#89817C211yesmaximal, characteristic, complemented
9C2×#89815C211yesmaximal, characteristic, complemented
10#11738364C2116yesmaximal, direct product factor
11C2×D7×#106C211yesmaximal, characteristic, complemented
12C2×#89628C211yesmaximal, characteristic, complemented
13C2×#89581C211yesmaximal, characteristic, complemented
14C2×#89577C211yesmaximal, characteristic, complemented
15C2×#89568C211yesmaximal, characteristic, complemented
16C2×#89563C211yesmaximal, characteristic, complemented
17C22×C7×Q16C2211yescharacteristic
18C22×C7×M16C2211yescharacteristic
19C2×C7×C22⋊Q8C2211yescharacteristic
20C2×C7×C22⋊Q8C2211yescharacteristic
21C2×#6509C2211yescharacteristic
22C2×#6509C2211yescharacteristic
23C2×Q8×Dic7C2211yescharacteristic
24C2×Q8×Dic7C2211yescharacteristic
25C2×C4×C22⋊D7C2211yescharacteristic
26C2×#6489C2211yescharacteristic
27C22×C4⋊Dic7C2211yescharacteristic
28C22×C8×D7C2211yescharacteristic
29#90330—24no—
30#90330C2218yes—
31#90326—24no—
32#90326C2218yes—
33C2×#6460—21no—
34C2×#6455—21no—
35C2×D7×C4⋊C4C2211yescharacteristic
36C2×D7×C4⋊C4C2211yescharacteristic
37C2×#6453C2211yescharacteristic
38C2×#6452—21no—
39C2×#6452—21no—
40C2×#6451C2211yescharacteristic
41C2×#6446—21no—
42C2×(C22⋊D7)⋊C4—21no—
43C2×#6442—21no—
44C2×#6441—21no—
45C7×#470C2218yescomplemented
46C2×C7×#106C2211yescharacteristic
47C2×C7×#103C2211yescharacteristic
48C2×C7×#103C2211yescharacteristic
49C2×#6409C2211yescharacteristic
50C2×#6409C2211yescharacteristic
51C2×#6409C2211yescharacteristic
52C2×#6409C2211yescharacteristic
53C2×C22⋊(C7⋊C8)C2211yescharacteristic
54#89960C2218yescomplemented
55#89956C2218yescomplemented
56#89899C2218yes—
57#89893C2218yescomplemented
58C2×(C2×D7)⋊C8C2211yescharacteristic
59C2×#6392C2211yescharacteristic
60C2×#6392C2211yescharacteristic
61C2×#6391C2211yescharacteristic
62C2×#6391C2211yescharacteristic
63C2×#6389C2211yescharacteristic
64C2×Dic7⋊C8C2211yescharacteristic
65#89817C2218yescomplemented
66#89815C2218yescomplemented
67C2×#6382C2211yescharacteristic
68C2×#6382C2211yescharacteristic
69C2×#6382C2211yescharacteristic
70C2×#6381C2211yescharacteristic
71D7×#106C2218yescomplemented
72#89628C2218yescomplemented
73#89581C2218yescomplemented
74#89577C2218yescomplemented
75#89568C2218yescomplemented
76#89563C2218yescomplemented
77C2×#3344—71nomaximal, Sylow
78C22×C7×Q8C2311yescharacteristic
79C22×C7×Q8C2311yescharacteristic
80C23×C4×C7C2311yescharacteristic
81C22×C22⋊D7D411yescharacteristic
82C23×Dic7—21no—
83C22×C4×D7—21no—
84C22×C4×D7—21no—
85C22×C4×D7C2311yescharacteristic
86C22×Dic14—21no—
87C2×C7×Q16—24no—
88C2×C7×Q16C2314yes—
89C2×C7×M16—24no—
90C2×C7×M16C2314yes—
91C22×C7×C8C2311yescharacteristic
92C22×C7×C8C2311yescharacteristic
93C7×C22⋊Q8—22no—
94C7×C22⋊Q8—22no—
95C7×C22⋊Q8C2314yes—
96C7×C22⋊Q8C2314yes—
97C2×C7×C4⋊C4—21no—
98C2×C7×C4⋊C4—21no—
99C2×C7×C4⋊C4C2311yescharacteristic
100C2×C7×C4⋊C4C2311yescharacteristic
101C2×C7×C22⋊C4—21no—
102C2×C7×C22⋊C4—21no—
103C2×C22⋊Dic7—21no—
104C2×C22⋊Dic7D411yescharacteristic
105#6509—22no—
106#6509—22no—
107#6509C2314yes—
108#6509C2314yes—
109Q8×Dic7—22no—
110Q8×Dic7—22no—
111Q8×Dic7C2314yes—
112Q8×Dic7C2314yes—
113C4×C22⋊D7D414yes—
114C4×C22⋊D7C2314yes—
115C2×(C2×D7)⋊C4—21no—
116C2×(C2×D7)⋊C4—21no—
117C2×(C2×D7)⋊C4D411yescharacteristic
118#6489—22no—
119#6489C2314yes—
120C2×C4⋊Dic7—21no—
121C2×C4⋊Dic7—22no—
122C2×C4⋊Dic7—21no—
123C2×C4⋊Dic7—21no—
124C2×C4⋊Dic7—21no—
125C2×C4⋊Dic7C2311yescharacteristic
126C2×C4⋊Dic7C2311yescharacteristic
127C2×C4⋊Dic7C2311yescharacteristic
128C2×C4⋊Dic7C2311yescharacteristic
129C2×C4⋊Dic7C2314yes—
130C2×Dic7⋊C4—21no—
131C2×Dic7⋊C4—21no—
132C2×Dic7⋊C4—21no—
133C2×Dic7⋊C4—21no—
134C2×Dic7⋊C4—21no—
135C2×Dic7⋊C4—21no—
136C2×Dic7⋊C4D411yescharacteristic
137C2×C4×Dic7—21no—
138C2×C4×Dic7—21no—
139C2×C4×Dic7—21no—
140C2×C4×Dic7C2311yescharacteristic
141C22×C7⋊C8C2311yescharacteristic
142C22×C7⋊C8C2311yescharacteristic
143C2×C8×D7—24no—
144C2×C8×D7C2314yes—
145#6460—28no—
146#6455—28no—
147D7×C4⋊C4—22no—
148D7×C4⋊C4—22no—
149D7×C4⋊C4C2314yes—
150D7×C4⋊C4C2314yes—
151#6453—22no—
152#6453C2314yes—
153#6452—28no—
154#6452—28no—
155#6451—22no—
156#6451C2314yes—
157#6446—28no—
158(C22⋊D7)⋊C4—28no—
159#6442—28no—
160#6441—28no—
161C7×#106C2314yes—
162C7×#103C2314yes—
163C7×#103C2314yes—
164#6409C2314yes—
165#6409C2314yes—
166#6409C2314yes—
167#6409C2314yes—
168C22⋊(C7⋊C8)C2314yes—
169(C2×D7)⋊C8C2314yes—
170#6392C2314yes—
171#6392C2314yes—
172#6391C2314yes—
173#6391C2314yes—
174#6389C2314yes—
175Dic7⋊C8C2314yes—
176#6382C2314yes—
177#6382C2314yes—
178#6382C2314yes—
179#6381C2314yes—
180C2×#554—71no—
181C2×#552—71no—
182#3344—716no—
183C2×#501—71no—
184C2×#484—71no—
185C2×#485—71no—
186C2×#483—71no—
187C2×#483—71no—
188C2×#479—71no—
189C2×#475—71no—
190C2×#470D711yescharacteristic, complemented
191C2×#467—71no—
192C2×#441—71no—
193C2×#435—71no—
194C2×#428—71no—
195C22×#106—71no—
196C24×C7C2×D411yescharacteristic
197C23×D7C2×D411yescharacteristic
198C2×C7×Q8—21no—
199C2×C7×Q8—21no—
200C2×C7×Q8—22no—
201C2×C7×Q8—22no—
202C2×C7×Q8—22no—
203C2×C7×Q8—22no—
204C2×C7×Q8C2412yes—
205C2×C7×Q8C2412yes—
206C22×C4×C7—22no—
207C22×C4×C7—22no—
208C22×C4×C7—21no—
209C22×C4×C7—21no—
210C22×C4×C7—21no—
211C22×C4×C7—21no—
212C22×C4×C7C2×D411yescharacteristic
213C22×C4×C7C2×D412yes—
214C22×C4×C7C2412yes—
215C22×C4×C7C2411yescharacteristic
216C2×C22⋊D7—24no—
217C2×C22⋊D7C2×D414yes—
218C22×Dic7—21no—
219C22×Dic7—21no—
220C22×Dic7—21no—
221C22×Dic7—21no—
222C22×Dic7—24no—
223C22×Dic7—82no—
224C22×Dic7C2×D411yescharacteristic
225C22×Dic7C2×D411yescharacteristic
226C22×Dic7C2×D411yescharacteristic
227C2×C4×D7—22no—
228C2×C4×D7—22no—
229C2×C4×D7—24no—
230C2×C4×D7—24no—
231C2×C4×D7—44no—
232C2×C4×D7—82no—
233C2×C4×D7C2×D412yes—
234C2×C4×D7C2412yes—
235C2×Dic14—24no—
236C2×Dic14—82no—
237C7×Q16—28no—
238C7×M16—28no—
239C2×C7×C8—22no—
240C2×C7×C8#4114yes—
241C2×C7×C8C2412yes—
242C2×C7×C8C2412yes—
243C7×C4⋊C4—21no—
244C7×C4⋊C4—24no—
245C7×C4⋊C4—24no—
246C7×C4⋊C4—21no—
247C7×C4⋊C4C2412yes—
248C7×C4⋊C4C2412yes—
249C7×C22⋊C4—24no—
250C7×C22⋊C4—24no—
251C22⋊Dic7—24no—
252C22⋊Dic7C2×D414yes—
253(C2×D7)⋊C4—24no—
254(C2×D7)⋊C4—24no—
255(C2×D7)⋊C4C2×D414yes—
256C4⋊Dic7—21no—
257C4⋊Dic7—24no—
258C4⋊Dic7—21no—
259C4⋊Dic7—21no—
260C4⋊Dic7—21no—
261C4⋊Dic7—24no—
262C4⋊Dic7—24no—
263C4⋊Dic7—24no—
264C4⋊Dic7C2412yes—
265C4⋊Dic7C2412yes—
266C4⋊Dic7C2412yes—
267C4⋊Dic7C2412yes—
268Dic7⋊C4—24no—
269Dic7⋊C4—24no—
270Dic7⋊C4—24no—
271Dic7⋊C4—24no—
272Dic7⋊C4—24no—
273Dic7⋊C4—24no—
274Dic7⋊C4C2×D414yes—
275C4×Dic7—24no—
276C4×Dic7—24no—
277C4×Dic7—24no—
278C4×Dic7C2×D412yes—
279C4×Dic7C2412yes—
280C2×C7⋊C8—22no—
281C2×C7⋊C8—22no—
282C2×C7⋊C8C2412yes—
283C2×C7⋊C8C2412yes—
284C8×D7—28no—
285C22×Q16C2×D711yescharacteristic
286C22×M16C2×D711yescharacteristic
287C23×C8—71no—
288#554—78no—
289#554—144no—
290#552—78no—
291#552—144no—
292C2×C4⋊Q8—71no—
293C2×#126—141no—
294C2×#125—71no—
295C2×#125—141no—
296C2×#125—141no—
297C2×#123—141no—
298C2×C22⋊Q8—71no—
299C2×C22⋊Q8—71no—
300C2×C22⋊Q8—141no—
301C2×C22⋊Q8—141no—
302C2×C22⋊Q8C2×D711yescharacteristic
303C2×C22⋊Q8C2×D711yescharacteristic
304C2×C4×Q8—71no—
305C2×C4×Q8—71no—
306C2×C4×D4—71no—
307C2×C4×D4—141no—
308C2×#117—71no—
309C2×#117—141no—
310C22×C4⋊C4—71no—
311C22×C4⋊C4—71no—
312C22×C4⋊C4—71no—
313#501—78no—
314#485—78no—
315#484—78no—
316#483—78no—
317#483—78no—
318#479—78no—
319#475—78no—
320#470C2×D718yescomplemented
321#467—78no—
322#441—78no—
323#435—78no—
324#428—78no—
325C2×#107—71no—
326C2×#107—71no—
327C2×#107—71no—
328C2×#106—71no—
329C2×#106—71no—
330C2×#106—71no—
331C2×#106—71no—
332C2×#106—71no—
333C2×#106—78no—
334C2×#106C2×D711yescharacteristic
335C2×C4⋊C8—71no—
336C2×#103—71no—
337C2×#103—71no—
338C2×#103—71no—
339C2×#103—71no—
340C2×#103C2×D711yescharacteristic
341C2×#103C2×D711yescharacteristic
342C2×C22⋊C8—71no—
343C2×C22⋊C8—71no—
344C2×#97—71no—
345C23×C7—22no—
346C23×C7—22no—
347C23×C7—22no—
348C23×C7C22×D412yes—
349C23×C7C22×D411yescharacteristic
350C22×D7—22no—
351C22×D7—22no—
352C22×D7#13714yes—
353C22×D7C22×D412yes—
354C7×Q8—22no—
355C7×Q8—22no—
356C7×Q8—22no—
357C7×Q8—22no—
358C7×Q8—42no—
359C7×Q8—42no—
360C2×C4×C7—22no—
361C2×C4×C7—24no—
362C2×C4×C7—22no—
363C2×C4×C7—22no—
364C2×C4×C7—22no—
365C2×C4×C7—22no—
366C2×C4×C7—22no—
367C2×C4×C7—22no—
368C2×C4×C7—42no—
369C2×C4×C7—42no—
370C2×C4×C7—42no—
371C2×C4×C7—42no—
372C2×C4×C7C22×D412yes—
373C2×C4×C7C22×D411yescharacteristic
374C2×C4×C7C2×#4112yes—
375C2×C4×C72−1+412yes—
376C2×C4×C7C2511yescharacteristic
377C22⋊D7—28no—
378C2×Dic7—22no—
379C2×Dic7—22no—
380C2×Dic7—22no—
381C2×Dic7—22no—
382C2×Dic7—22no—
383C2×Dic7—22no—
384C2×Dic7—22no—
385C2×Dic7—42no—
386C2×Dic7—42no—
387C2×Dic7—42no—
388C2×Dic7—42no—
389C2×Dic7—84no—
390C2×Dic7C22×D412yes—
391C2×Dic7C22×D412yes—
392C2×Dic7C22×D412yes—
393C4×D7—24no—
394C4×D7—22no—
395C4×D7—22no—
396C4×D7—48no—
397C4×D7—84no—
398Dic14—84no—
399C7×C8—22no—
400C7×C8C2×#4114yes—
401C7⋊C8—22no—
402C7⋊C8—22no—
403C22×Q8—141no—
404C22×Q8C22×D711yescharacteristic
405C22×Q8C22×D711yescharacteristic
406C22×D4—71no—
407C23×C4—71no—
408C23×C4—141no—
409C23×C4—141no—
410C23×C4—141no—
411C23×C4C22×D711yescharacteristic
412C2×Q16—24no—
413C2×Q16C22×D714yes—
414C2×M16—24no—
415C2×M16C22×D714yes—
416C22×C8—71no—
417C22×C8—71no—
418C22×C8—74no—
419C22×C8—144no—
420C22×C8C22×D711yescharacteristic
421C22×C8C22×D711yescharacteristic
422C4⋊Q8—74no—
423C4⋊Q8—142no—
424#126—148no—
425#125—74no—
426#125—142no—
427#125—148no—
428#125—148no—
429#123—148no—
430C22⋊Q8—22no—
431C22⋊Q8—22no—
432C22⋊Q8—74no—
433C22⋊Q8—74no—
434C22⋊Q8—148no—
435C22⋊Q8—148no—
436C22⋊Q8—142no—
437C22⋊Q8—142no—
438C22⋊Q8C22×D714yes—
439C22⋊Q8C22×D714yes—
440C4×Q8—74no—
441C4×Q8—74no—
442C4×Q8—142no—
443C4×Q8—142no—
444C4×D4—74no—
445C4×D4—74no—
446C4×D4—148no—
447#117—74no—
448#117—148no—
449#117—142no—
450C2×C4⋊C4—21no—
451C2×C4⋊C4—21no—
452C2×C4⋊C4—71no—
453C2×C4⋊C4—71no—
454C2×C4⋊C4—71no—
455C2×C4⋊C4—71no—
456C2×C4⋊C4—74no—
457C2×C4⋊C4—71no—
458C2×C4⋊C4—74no—
459C2×C4⋊C4—74no—
460C2×C4⋊C4—142no—
461C2×C4⋊C4—142no—
462C2×C4⋊C4—141no—
463C2×C4⋊C4—141no—
464C2×C4⋊C4—141no—
465C2×C4⋊C4—141no—
466C2×C4⋊C4—141no—
467C2×C4⋊C4—141no—
468C2×C4⋊C4—141no—
469C2×C4⋊C4—141no—
470C2×C4⋊C4—141no—
471C2×C4⋊C4—141no—
472C2×C4⋊C4—142no—
473C2×C4⋊C4C22×D711yescharacteristic
474C2×C4⋊C4C22×D711yescharacteristic
475C2×C22⋊C4—21no—
476C2×C22⋊C4—21no—
477C2×C22⋊C4—71no—
478C2×C22⋊C4—71no—
479C2×C22⋊C4—141no—
480C2×C22⋊C4—141no—
481C2×C22⋊C4—141no—
482C2×C42—71no—
483C2×C42—141no—
484C2×C42—141no—
485C2×C42—141no—
486#107—74no—
487#107—74no—
488#107—74no—
489#106—74no—
490#106—74no—
491#106—74no—
492#106—74no—
493#106—74no—
494#106C22×D714yes—
495C4⋊C8—74no—
496#103—74no—
497#103—74no—
498#103—74no—
499#103—74no—
500#103C22×D714yes—
501#103C22×D714yes—
502C22⋊C8—74no—
503C22⋊C8—74no—
504#97—74no—
505C22×C7—22no—
506C22×C7—22no—
507C22×C7—22no—
508C22×C7—44no—
509C22×C7#54712yes—
510C22×C7C2×#13712yes—
511C22×C7#57712yes—
512C22×C7C23×D411yescharacteristic
513C2×D7—28no—
514C2×D7—22no—
515C2×D7—22no—
516C2×D7C2×#13714yes—
517C4×C7—22no—
518C4×C7—42no—
519C4×C7—42no—
520C4×C7—42no—
521C4×C7—42no—
522C4×C7#54712yes—
523C4×C7C22×#4111yescharacteristic
524C4×C7C2×2−1+411yescharacteristic
525Dic7—22no—
526Dic7—22no—
527Dic7—22no—
528Dic7—42no—
529Dic7—42no—
530Dic7—42no—
531Dic7—42no—
532C24—71no—
533C24D4×D711yescharacteristic
534C2×Q8—21no—
535C2×Q8—21no—
536C2×Q8—22no—
537C2×Q8—22no—
538C2×Q8—22no—
539C2×Q8—22no—
540C2×Q8—144no—
541C2×Q8—562no—
542C2×Q8C23×D712yes—
543C2×Q8C23×D712yes—
544C2×D4—74no—
545C2×D4—144no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—71no—
553C22×C4—71no—
554C22×C4—71no—
555C22×C4—72no—
556C22×C4—72no—
557C22×C4—144no—
558C22×C4—144no—
559C22×C4—142no—
560C22×C4—142no—
561C22×C4—141no—
562C22×C4—141no—
563C22×C4—141no—
564C22×C4—141no—
565C22×C4—144no—
566C22×C4—284no—
567C22×C4—562no—
568C22×C4—562no—
569C22×C4D4×D712yes—
570C22×C4D4×D711yescharacteristic
571C22×C4C23×D712yes—
572C22×C4C23×D711yescharacteristic
573Q16—28no—
574M16—28no—
575C2×C8—22no—
576C2×C8—72no—
577C2×C8—72no—
578C2×C8—142no—
579C2×C8—142no—
580C2×C8—148no—
581C2×C8#115914yes—
582C2×C8C23×D712yes—
583C2×C8C23×D712yes—
584C4⋊C4—24no—
585C4⋊C4—24no—
586C4⋊C4—21no—
587C4⋊C4—21no—
588C4⋊C4—74no—
589C4⋊C4—72no—
590C4⋊C4—72no—
591C4⋊C4—72no—
592C4⋊C4—72no—
593C4⋊C4—144no—
594C4⋊C4—144no—
595C4⋊C4—144no—
596C4⋊C4—144no—
597C4⋊C4—144no—
598C4⋊C4—144no—
599C4⋊C4—144no—
600C4⋊C4—144no—
601C4⋊C4—144no—
602C4⋊C4—141no—
603C4⋊C4—141no—
604C4⋊C4—144no—
605C4⋊C4—141no—
606C4⋊C4—141no—
607C4⋊C4C23×D712yes—
608C4⋊C4C23×D712yes—
609C22⋊C4—24no—
610C22⋊C4—24no—
611C22⋊C4—74no—
612C22⋊C4—74no—
613C22⋊C4—144no—
614C22⋊C4—144no—
615C22⋊C4—144no—
616C42—72no—
617C42—72no—
618C42—144no—
619C42—144no—
620C42—144no—
621C2×C7—42no—
622C2×C7#334414yescomplemented
623C2×C7C2×#54711yescharacteristic
624C2×C7C22×#13711yescharacteristic
625C2×C7C2×#57711yescharacteristic
626D7—24no—
627C23—22no—
628C23—22no—
629C23—22no—
630C23—74no—
631C23—72no—
632C23—142no—
633C23—142no—
634C23C2×D4×D712yes—
635C23C2×D4×D711yescharacteristic
636Q8—22no—
637Q8—22no—
638Q8—22no—
639Q8—22no—
640Q8—42no—
641Q8—42no—
642Q8—564no—
643D4—148no—
644C2×C4—22no—
645C2×C4—24no—
646C2×C4—22no—
647C2×C4—22no—
648C2×C4—22no—
649C2×C4—22no—
650C2×C4—22no—
651C2×C4—22no—
652C2×C4—42no—
653C2×C4—42no—
654C2×C4—42no—
655C2×C4—42no—
656C2×C4—72no—
657C2×C4—72no—
658C2×C4—72no—
659C2×C4—142no—
660C2×C4—142no—
661C2×C4—142no—
662C2×C4—144no—
663C2×C4—142no—
664C2×C4—142no—
665C2×C4—142no—
666C2×C4—142no—
667C2×C4—142no—
668C2×C4—142no—
669C2×C4—288no—
670C2×C4—282no—
671C2×C4—282no—
672C2×C4—282no—
673C2×C4—282no—
674C2×C4—564no—
675C2×C4—564no—
676C2×C4C2×D4×D712yes—
677C2×C4C2×D4×D711yescharacteristic
678C2×C4C2×#115912yes—
679C2×C4#655412yes—
680C2×C4C24×D711yescharacteristic
681C8—22no—
682C8—142no—
683C8—142no—
684C8C2×#115914yes—
685C7C2×#334411yescharacteristic, complemented, Sylow
686C22—22no—
687C22—22no—
688C22—22no—
689C22—44no—
690C22—74no—
691C22—142no—
692C22—142no—
693C22—148no—
694C22#9030212yes—
695C22D7×#13712yes—
696C22#9046912yes—
697C22C22×D4×D711yescharacteristic
698C4—22no—
699C4—42no—
700C4—42no—
701C4—42no—
702C4—42no—
703C4—142no—
704C4—142no—
705C4—142no—
706C4—282no—
707C4—282no—
708C4—282no—
709C4—282no—
710C4#9030212yes—
711C4C22×#115911yescharacteristic
712C4C2×#655411yescharacteristic
713C2—42no—
714C2—144no—
715C2#1173836414yesdirect product factor
716C2C2×#9030211yescharacteristic
717C2C2×D7×#13711yescharacteristic
718C2C2×#9046911yescharacteristic
subgroupG/H
centerC23C2×D4×D7
commutator, cosocleC2×C4×C7C25
FrattiniC2×C4C24×D7
FittingC2×C7×#470C2
socleC23×C7C22×D4
prime radicalC22×C22⋊D7D4
hypercenterC2×#470D7
hypocenterC7C2×#3344
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#470

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
3. C2×C7×#470C2semidirect
4. C2×#89960C2semidirect
5. C2×#89956C2semidirect
7. C2×#89893C2semidirect
8. C2×#89817C2semidirect
9. C2×#89815C2semidirect
10. #11738364C2direct (N × H)
11. C2×D7×#106C2semidirect
12. C2×#89628C2semidirect
13. C2×#89581C2semidirect
14. C2×#89577C2semidirect
15. C2×#89568C2semidirect
16. C2×#89563C2semidirect
45. C7×#470C22semidirect
54. #89960C22semidirect
55. #89956C22semidirect
57. #89893C22semidirect
65. #89817C22semidirect
66. #89815C22semidirect
71. D7×#106C22semidirect
72. #89628C22semidirect
73. #89581C22semidirect
74. #89577C22semidirect
75. #89568C22semidirect
76. #89563C22semidirect
190. C2×#470D7semidirect
320. #470C2×D7semidirect
622. C2×C7#3344semidirect
685. C7C2×#3344semidirect
715. C2#11738364direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#903302
C2×#903262
C2×C7×#4702
C2×#899602
C2×#899562
C2×#898992
C2×#898932
C2×#898172
C2×#898152
#117383642
C2×D7×#1062
C2×#896282
C2×#895812
C2×#895772
C2×#895682
C2×#895632
C2×#33447